$\Large \int\frac{dx}{\sin(x-a)\sin(x-b)}$ is equal to $$\begin{array}{1 1}(A)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C & (B)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \\(C)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C &(D)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \end{array}$$

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